Every sci fi show in history has expanded events that took place 50-70 years in the past. Some have had entire arcs and seasons or even the entire show built around the past. Period is not "completely different," neither is showing the leadership out on missions much different from showing the non-leaders out on missions. The actions taken and motivations involved are pretty much the same.

Now... there are ways to differentiate this show, and they may indeed be ways that they are contemplating, but based on the Agent Carter short, the only difference is set dressing and whether people have cell phones.

If they focus on something other than SHIELD's missions, I think they will have a strong unique flavor. But they may not be going for that... the goal might be precisely to have two sides of the same coin, and live of the synergy between them. That might be cool as well.

It could be different then AOS because maybe with SHIELD under the reign of Peggy and Howard Stark (as I said earlier) they could track the untrackable human bad guys (such as former Nazis living in South America) that the other government agencies have been unable to track.

Remember, at the end of TFA, the war has ended. Real life history says that a bunch of Ex-Nazis disappeared only to resurface in Latin America years later with some of them having died in exile in South America. That could be a focal point of Agent Carter's Shield at least early on. There could also be an emphasis on Hydra and Communist/Soviet agents and the show could also be a story to determine the whereabouts of Red Skull. Now if this show goes on for a long time, well into the 1980's as the timeline, SHIELD could shift to Superhumans.

On Agents of Shield, the focus is on aliens and superhumans.

I don't know if Marvel wants to go for Peggy's Shield as Nazi/HYRDA/Communist hunters early on, but who knows. It would be different than Agents of Shield, but yet tie into it too.